Derived equivalence as iterated tilting

摘要

Let A and B be two finite dimensional algebras derived equivalent to a connected hereditary noetherian category $cal H$ with a tilting complex. We prove that there exists a sequence of finite dimensional algebras $Lambda _0, Lambda _1,ldots ,Lambda _m$ and tilting modules $T_{Lambda _0},T_{Lambda _1},ldots ,T_{Lambda _{m-1}}, mgeqq 1$ , such that $Lambda _0=A, Lambda _m= B$ , and $Lambda _{i+1}= {rm End}, {T!}_{A_i}$ for $0 leqq i le m$ .